Distortion correction in wave transmission



vuul hll HUUHI J. G. KREER, JR

DISTORTION CORRECTION IN WAVE TRANSMISSION Filed Aug. 10, 1957 INVENTORJGiE WJF! BY J ATTORNEY f'l'eqaency 1%. 7

Patented Dec. 20, 1938 UNITED STATES search H001:

DISTORTION CORRECTION IN WAVE TRANSDIIS SION John G. Kreer, Jr.,Bloomfield, N. J., assignor to Bell Telephone Laboratories,Incorporated, New York, N. Y., a corporation of New York ApplicationAugust 10,

18 Claims.

This invention relates to communication systems and more especially,though not exclusively, to such systems as are identified as broadbandtelevision circuits or as carrier telephone circuits,

in which latter case a plurality of channels are used on a singletransmission medium for sendingout independent messages. One type ofcircuit of this kind, for example, would be that known as the coaxialconductor. The invention also relates to systems of the naturedescribed, in which a large number of repeaters are connected in tandem.

In spite of the great care which is used in the design and manufactureof such repeaters, there is present in the output of any one repeater acertain small amount of modulation product.

T; While the amount of modulation in any one repeater may be small, ifthe system comprises a large number of repeaters in tandem, such asseveral hundred, then the cumulative effect may become substantial. Thetype of modulation which is especially to be guarded against is thatknown as interchannel modulation, although intrachannel modulation mayalso need consideration.

This invention relates to methods and means for maintaining as low aspossible at the terminal station the ratio of modulation products tosignal intensity.

In a transmission system with repeaters it is the usual practice to makethe amplification at each repeater sufficient to just 9f: l .thenlossdue to attenuation in one repeater section of the cable. Thus, afterpassing through 11. repeater sections, the signal strength has beenunchanged. The modulation products, however, being introducedadditionally at each repeater station tend to increase as the number ofrepeaters in the line increases. Thus, in one case measured there was 40a 12-channel telegraph cable with '70 repeaters in tandem 25 milesapart. The modulation voltage at the output was found to besubstantially 70' times the modulation voltage of one repeater. Thepurpose of my invention is a method and means whereby this modulationvoltage may be kept to a much lower value.

While the above example related to a telegraph system, substantially thesame results would hold for telephone systems. Thus in a recentlydeveloped multiplex system, using a special cable, known as the coaxialcable, it is possible to transmit simultaneously a very large number ofchannels which may extend to the number of 500 to 1,000 telephonechannels. In such a system the repeaters may have a spacing of about 5miles 1937, Serial No. 158,295

or less and on a 1,000-mile circuit there would then be involved atleast 800 repeaters. If the inter-modulation products follow the lawindicated by the experiment referred to above, it will either becomeexcessive in amount or will require extraordinarily careful design ofrepeaters to keep down the modulation generated in any one repeater.

For a better understanding of the invention one may consider first asingle amplifier. For an ideal amplifier (which is a physicalimpossibility) it is assumed that the output is a faithful copy orreplica of the input voltage except as enlarged and except as it may bedelayed. Due to unavoidable non-linearity, harmonics and other undesiredproducts of modulation are present and will be represented as voltagevariations in the output not present in the input but still in thesignal frequency band. From the standpoint of how these products ofmodulation combine as a function of the number of repeaters, it will benecessary to distinguish and consider separately the even and the oddorder products of modulation. For the purposes of this discussion, itwill be sufiicient to consider only the second order products and thethird order products of modulation.

Consider a resistance line of loss L followed by a fiat gain amplifierof gain G, and consider a group of such identical units in tandem. Let Xbe the input at the transmitting end of the line which attenuates to a:in passing through the first section of line so that the input at thefirst repeater is represented by :c. The output of the amplifier may berepresented by X+k2r +ka$ (1) It will be observed that poling orreversing the input of the repeater does not change kzr but does reversethe other two terms given above. The input of this amplifier is notpoled.

Passing to the second amplifier, its input is where L is in napiers. Theoutput of the second amplifier is the amplified output due to the term:2,

namely, X+kzx +k3r plus the distortion introduced by the secondamplifier which is (k2r +k3:n It will now be observed that bypoling theinput to the second amplifier the second order terms cancel each otherin the output of the amplifier but the third order terms do not, so thatthe output of the second amplifier is X27c3:r Thus, in the absence ofphase shift in either line or amplifier, and in the presence of flatloss and fiat gain with frequency, if every other amplifier is poledthen with an even number of amplifiers the even order modulationproducts are theoretically zero and the odd order modulation voltageproducts are equal in amplitude to those of a single amplifiermultiplied by the number of amplifiers. Thus, the modulation voltageproducts for these terms add up arithmetically and the modulation poweroutput is given by P=n E where E is the modulation voltage set up by onerepeater.

If the resistance line in the previous example is replaced by atelephone cable for which the velocity of transmission of a wave is thesame for all frequencies, then there will be a time delay as one passesover a repeater cable section but the wave shape at the input of onerepeater is identically the same as the wave shape at the output of theprevious repeater. Such a condition is quite closely approximated over awide frequency band in the so-called coaxial cable and it will beapparent from what has been said heretofore that by suitable poling atthe successive repeaters it is possible to balance out even order termsbut that the odd order modulation voltage terms are those of a singleamplifier multiplied by the number of amplifiers. For such an idealtransmission medium, the actual phase shift, expressed in radians, asone passes over a repeater section is proportional to the frequency andwould be represented by a phase frequency characteristic which is astraight line passing through zero, as indicated by curve A of Fig. 7.

If the straight line phase relationship stipulated above is notsatisfied then the rule previously cited is no longer valid. Assume, forexample,

that by additional phase retardation at certain points on thetransmission line, such as at the input of each repeater, the phasefrequency characteristic departs from the previous straight linerelationship. Assume, also, that X is a sine wave. The output of thefirst amplifier of the string is not afi'ected by these changes. neitheris the signal input to the second amplifier to the extent that theharmonics generated in the second amplifier depend only upon thefundamental applied. Added to them, however. are the amplified harmoniesfrom the first amplifier wh ch by comparison to the original conditionare retarded in phase by the input equalizer of the second amplifier.Assuming even numbered amplifiers are poled. if the amplified secondharmon c as produced in the first amplifier originally opposed orcanceled the second harmonic produced in the second amplifier, then withthe added phase retardation to the frequency 2 over that to thefrequency f in the input equalizer this opposing action or balance isimpaired to an extent depending upon the amount of phase incrementintroduced. In a similar way, when considering a third order productsuch as one of frequency 3f. if without the extra phase shift in theinput equalizer to 3) the effect of the 3] component from the firstamplifier was to add precisely in phase with the 3 component produced bythe second amplifier, then with the extra phase shift the vector sum ofthe two is less. Similar effects take place at succeeding amplifiers.

As pointed out above, the invention is especially but not exclusivelyapplicable to a transmission system in which a wide frequency band isdivided into a large number of signal channels. In this case the widthof any one channel band is usually small compared to the total signalingband but repeaters are used in common by all or a large number of thechannels. The non-linearity of the repeaters will give rise to sum anddifference frequencies commonly called modulation frequencies, ormodulation products as the term has been used above. Any one modulationfrequency may be obtained in numerous ways. Thus, for the summationfrequency ja=f1+j2, f1 and f2 may take on a large variety of values buta particular pair of values may be spoken of as one modulation sourcefor the frequency f3 and there will be many such sources in the broadband, giving rise to a particular modulation frequency f3 in anyspecific channel. Furthermore, while in any one channel the modulationfrequencies will be distributed over all frequencies in that band, theband is relatively so narrow that for most considerations it is feasibleto treat all the modulation frequencies in that channel band as being ofone frequency.

The invention will be better understood by reference to the followingspecification and the accompanying drawing, in which:

Fig. 1 shows a transmission line with a large number of repeatersconnected in tandem, each repeater being provided with a phaseequalizing or phase shifting device the characteristic of which will bedescribed later;

Fig. 2 shows a modification of Fig. 1;

Figs. 3 and 4 are diagrams to assist in the explanation of my invention;

Figs. 5 and 6 relate to means to compensate for certain variations;

Fig. 7 is a diagram showing certain phase frequency characteristicsapplicable to an understanding of my invention;

Fig. 8 shows a physical form which the phase equalizers of Fig. 1 maytake on; and

Fig. 9 relates to certain compensating arrangements.

Referring more particularly to Fig. 1, there is shown a transmittingstation T1 and a receivin station T2 joined by a transmission line. suchas a coaxial cable. In this line there are numerous repeaters R intandem and in accordance with well established practice. the gain ofeach repeater is set at such a value as to just compensate for the lossin the previous section of cable so that at the end of the line theintensity of the signal is substantially the same as at the transmittingend. In each repeater section there is a phase equalizer PE. here shownat the repeater input, which serves the function of introducing arelative phase shift among the currents of d fferent frequency inaccordance with a plan to be shown later. For the purpose of s mplic tyit will be assumed that all repeater sections ncluding.

the phase equalizer) are identical. Let the modulation voltage generatedin one repeater be E, this modulation product arising from certainsignal frequencies. When these s gnal and modulation voltages havearrived at the input of the next repeater, having passed through a cablesection and a phase equalizer. the phase of the modulation productvoltage with respect to its generating signal voltages will have beenmodified. The signal passing through the second repeater will give r seto another element of modulation voltage of value E bearing the samephase relationship to the generating signal voltages as existed betweenthe first modulation product and the signal at the output of the firstrepeater and this second generated modulation product will be out ofphase with that which arrived from the first repeater n Search Room andwas amplified in the second repeater. This phase difference will beindicated by 'and will be assumed the same for each section. On thisbasis the resulting modulation voltage at the end of n repeaters will beThis is a geometric series which is readily summed up to be:

At the receiving terminal the particular phase of the modulation productis not of importance but the magnitude is; and the magnitude of themodulation voltage is readily obtained from Equation 2 as Thus themaximum modulation, without regard to the number of repeaters, is givenby and for some values of n will be less.

The value of the modulation voltage generated in one repeater from acertain modulation source has been representedby E. The total modulationproduct at the end of the line due to this source will of course begreater. If the amount of modulation voltage from that source permittedfor the whole system is E1 at the terminal station then the system willbe operative regardless of the number of repeaters if we intentionallyintroduce phase distortion at each repeater of such nature as to makethe modulation phase increment 0 satisfy the relationship If new thereare several sources instead of one, they will, in general, benon-coherent. The combination will, therefore, yield a total modulationpower output equal to the sum of the power outputs of the individualsources, and thus the modulation voltage will be given by where m is thenumber of sources, 12 the number of repeaters and E is assumed to be thesame for 7:1 Sill. '2" y If the 0,s are commensurable, then we may findthere is no value of M which can satisfy this condition and the actualmaximum of modulation product will be less than this power bound.However, Equation 9 still gives an upper bound of the modulationproduct. By writing Er for E in Equation 9, the limit of totalmodulation voltage M is found for a given signal channel where Er is themodulation voltage in that channel generated between two adjacentintermediate points due to any one source for any one frequency and 9:is the phase displacement between that voltage and the analogous voltagearriving at the first of the said two intermediate points. Thus,

2. sin

It is thus seen that we can place an upper limit upon the amount ofmodulation interference voltage which may occur in a system byintroducing, if necessary, additional and enough phase distortion bymeans of a suitable network at regular intervals, preferably at eachrepeater, so that if E is the generated voltage for one source in onerepeater and E1 the permissible modulation for the complete system thenFurthermore, if this phase distortion is sufiicient to be objectionablefrom a transmission standpoint, it may be equalized at either endofthesystem or at any point without in any way affecting the modulation.

The analysis given above may be made more clear by the graphicalrepresentation of Fig. 3. If the vector AB represents the modulationvoltage from a particular modulation source and at the output of thefirst repeater, then there will be an equal modulation product generatedin the second repeater but because of the phase distortion presentbetween the output of the first and the output of the second repeaterthis second vector will be out of phase with the first one by the angle0 and would be represented in Fig. 3 by the vector BC. The. resultant ofthese two vectors obviously is the line joining the points A and C. Ifadditional repeaters are considered, then the vector diagram is obtainedby continuing the drawing of the vectors each with a phase increment 0and it will be seen that the maximum value which the modulation voltagecan attain is that given by the diameter of the circumscribing circle,this circle being the one identified as passing through three suchpoints as A, B and C. The condition for maximum value of the modulationproduct in the situation-described heretofore corresponds to thediameter of the circle. The possibility is envisaged of reducing thisactual modulation product to a value substantially below thatcorresponding to the diameter of the circle, but the insignificant pointis that it can be kept to a and to the extent that can be controlled themaximum modulation voltage can be controlled.

The question now arises as to what phase characteristic should be givento a repeater section in order that the results indicated by theanalysis shall be attainable. The question is complicated by the factthat in any one channel any and all the frequencies available for theband width of that channel will be represented at one time or another inthe signal frequencies and that superposed on these signal frequenciesare the same frequencies appearing as modulation frequencies from onesource or another, such as inter-channel modulation.

I find that the conditions given above, namely, that the maximummodulation present shall not exceed a value corresponding to the circleof Fig. 3, can be obtained with considerable latitude as to the phasefrequency characteristic of the repeater section (including the phaseequalizer), but of the numerous ones possible the one shown by curve Cof Fig. 7 I find to be simple. in form and possible of realization. Itis especially effective in case the second order harmonics areimportant. The curve C of Fig. 7 is the sum of the curves A and B. CurveA represents the phase frequency characteristic of the line of therepeater section, which in the case of some lines such as a coaxialcable may be substantially a straight line passing through the origin.Curve B represents the phase frequency characteristic of the phaseequalizer which is so designed that curve C is one of a family ofparabolas each of which passes through the origin. If curve A is astraight line then curve B is itself a parabola with the apex at theorigin. The curve C being parabolic may be represented by the equationHaving determined the desired form of phase frequency characteristic asrepresented by such a curve as that of Fig. '7, it now becomes feasibleto design a network which taken alone or in combination with the cablesection will give that particular phase frequency characteristic. Thematter of design of such a network does not constitute a part of myinvention but the procedure for such design is set forth in theliterature in such articles as, for example, that of Zobel, in the BellSystem Technical Journal, vol. 7, page 488, or patent to Zobel 1,603,305of October 19, 1926. Fig. 8 illustrates one type of network commonlycalled an all-pass structure, which has great flexibility so far asphase frequency characteristic is concerned. The impedances Z1 and Z2 inthis network may consist of inductances or capacitances or both and eachimpedance may be a simple unit or a complex one. By proper choice of thecapacities and inductances assigned to each of the impedances of thenetwork, phase frequency characteristics of a wide range may beobtained.

In the above considerations it has been assumed that all repeater spansare identical, both as to the amount of modulation generated and as tothe phase increment of the product. This condition will, of course,never be realized in practice since, in general, some of the phaseincrement will be contributed by the line and hence will vary with thelength of the span. Also, the amount of modulation generated will varywith variations in vacuum tubes, circuit elements, etc. However, theextent of the variation will be limited due to the fact that allpossible lengths of span are not used but only those between certainlimits and by the fact that inspection of repeaters will reject any inwhich the modulation exceeds a certain amount. The effect of thevariations can be determined to a certain extent by a simple geometricalmethod indicated in Fig. 4 and thus the tolerable limits of variationmay be determined. If the repeater sections are identically the same inevery respect then the vector diagram of Fig. 3 is appropriate. If weconsider the case of variable E and 0, we may construct the circlescorresponding to the maximum value of E with the minimum value of 0 andthe minimum value of E with the maximum value of 0. Such vector diagramswith their circumscribing circles are represented in Fig. 4. The actualresultant will not, in general, lie far outside the region between thetwo circles regardless of the distribution of the 0s and the E's.

In the event that the phase shift for one section, because oftempertaure or humidity variations as they effect the cable or becauseof aging of the repeaters, is larger than is desired, such variationsmay render it desirable to make the phase equalizer at the input of arepeater or elsewhere variable and controlled in sucha manner as tocompensate for the variations arising otherwise in the repeatersections. A large variety of circuit arrangements may be used for thispurpose and one such arrangement is shown in Fig. 5 this being forillustrative purposes only. In Fig. 5 there is shown at the beginning ofone repeater section a pilot signalsgurce which may consist of agenerator of two frequencies f1 and 12, these being chosen as typicalfrequencies for which compensation should be made. Signals of thesefrequencies are impressed on the repeater section and are shown as beingtaken off at the output of the repeater R by sharply selective filterssuch as crystal filters CF1 and CFz. These two frequencies may now beamplified and passed through some suitable detecting device D which willhave an output the phase and amplitude of which are dependent on thephase relationship between I: and f2 and they may be used to controlsome device such as a motor M to change the phase equalizer by an amountsufficient to compensate for the variation which has taken place in therepeater section. The motor, for example, may be used to control avariable air condenser.

While the detecting device D may take on a large variety of forms, onesuch form is shown in Fig, 6 for illustrative purposes. Here the outputof the filter CFl is impressed by means of a transformer on a circuitcomprising two rectifiers I and 2, such as copper-oxide rectifiers. Thecircuit also includes an impedance such as the resistances 3 and 4.Bridged across this particular network is a transformer the primary ofwhich is supplied from the output of the filter CFz. The direction offlow of the rectified current in the resistance will be in the onedirection or the other depending upon whether there has been a shift inphase in one direction or the other of one of the pilot signals withrespect to the other.

Again, if we find that the repeaters are not all identical even withsuch compensation as just described, we may consider the totalmodulation as being made up of two parts, a systematic part equal to theaverage value and a random deviation from that value. The systematicpart will add up in the manner already described. The random deviationswill have a most probable value equal to the square root of the numberof repeaters times the standard deviation and will have a maximum valueequal to the number of repeaters times the maximum possible deviation.The resultant of these deviations must add vectorially to the resultantof the systematic portion which has already been discussed. If thenumber of repeaters is large this contribu tion of the deviations mayconceivably be fairly large compared to the systematic portion, and itis, therefore, desirable to reduce as much as possible the deviations ofthe modulation generated in the repeaters. Supplemental then to suchother compensations as may be introduced, such reduction may beaccomplished by the use of feedback amplifiers in which the gain of theamplifier tube is varied, either manually or automatically, in such away as to maintain a constant modulation coefficient from repeater torepeater. Fig. 9 shows one embodiment of this idea. Here a typicalrepeater section with a stabilizing feedback circuit N is indicated. Inseries with the cathode is shown a variable resistance I 6 common toboth the input and output circuits of the repeater and serving as alocal feedback circuit. By varying this resistance, and thus the gain ofthe repeater, its characteristic may be altered in such a way, manuallyor automatically, as to maintain a constant modulation coefficient forthe repeater section.

While the invention has been described in terms of the circuit of Fig. 1it is to be understood that many variations may be introduced, thus,whereas in Fig. 1 a phase equalizer is shown in front of each repeaterone may find it desirabl t use phase equalizer for a group of repeaterssuch as shown in Fig. 2. Also the compensations referred to above may bemade at each repeater or at each phase equalizer or in connection withgroups of these. The decision as to the frequency of spacing of phaseequalizers or of compensating means will depend upon the magnitude ofthe effects desired or the effects to be compensated for.

What is claimed is:

1. In a signal transmission system comprising a transmission line with aplurality of repeaters in tandem, the method of reducing the ratio ofmodulation products to signal intensity which consists in introducingphase distortion at a plurality of points, the phase distortion being ofsuch character as to produce similar angular shift, in the samedirection, of the modulation voltages produced in successive repeatersand to keep the maximum resultant modulation voltage for any onefrequency below a definite value regardless of the number of repeaters.

2. In a signal transmission system comprising a transmission line with aplurality of repeaters in tandem, the method of reducing the ratio ofmodulation products to signal intensity which consists in introducingphase distortion at a plurality of points, the phase distortion being ofsuchacharacter that the modulation voltage from repeater to repeaterprogressively rotates in the same angular direction and the resultantvalue of the modulation voltage changes in a substantially cyclicalmanner.

modulation voltage for any one frequency below a definite value given bywhere E is the modulation voltage generated in one repeater and is thephase distortion for that frequency between two of said points adjacentto each other.

4. In a signal transmission system comprising a transmission linwith aplurality of repeaters 'n tandem, each giving rise to iT rnodula tionvoltag hiclrfor any frequency from any one modulation source is given byE, the method of keeping the modulation voltage for the line at thatfrequency below a predetermined value E1 in excess of E which consistsin introducing in connection with gchrepeater section a phasefrequencyfdistortion 0 for that frequency of such value that 0 51112 isgreater than 2 1 5. The combination ofclaim 4 characterized by the factthat the phase distortion is introduced at each repeater.

6. In a signal transmission system comprising a transmission line with aplurality qfrepeaters in tandem" and adapted for a 'pliirality'of signalchannels, ,,the method of reducing the ratio of modulation products tosignal intensity-which consists in introducing phase frequencydistortion at a plurality of uniformly spaced intermediate points, thephase frequency distortion being of such character that the totalmodulation voltage M in a given signal channel is equal to or less thanwhere Er is the modulation voltage in that channel generated between twoadjacent intermediate points due t o anyone source for any one frequencyand 62 is the phase displacement between thatvoltage and the analogousvoltage arriving at the first of the said two intermediate points.

7. In a signal transmission system comprising a transmission line with aplurality of repeaters I intandem, each repeater giving rise tomodulation voltages, phase distorting means at a plurality of pointssubstantially equally spaced electrically and dividing the line intoequal sections, the phase frequency characteristic of the distortingmeans with that of its section being such that the modulation voltage atany one frequency generated in one section will be displaced in phase bythe amount 0 with respect to the same modulation voltage arriving atthat section, where 0 is given by E is the modulation voltage generatedin one section and E1 is the maximum modulation voltage at thatfrequency permitted in the transmission line.

8. In a signal transmission system comprising a transmission line with aplurality of repeaters in tandem, each repeater giving rise tomodulation voltages, phase distorting means at a plurality of pointssubstantially equally spaced electrically, dividing the line into equalsections, the phase frequency characteristic of the distorting meanswith that of its section being a parabola.

9. In a signal transmission system comprising a transmission line with aplurality .of r.ep aters in tandem, each repeater giving rise tomodulation voltages, phase distorting means at a plurality of pointsequally spaced electrically, dividing the line into equal sections, thephase frequency characteristic of the distorting means with that of itssection being one of a family of parabolas passing through the origin ofthe phase frequency diagram for the section.

10. The combination of claim 8 characterized by the fact that one of thephase distorting means is placed in each repeater section.

11. The combination of claim 8 characterized by the fact that one of thephase distorting means is introduced at each repeater.

12. In a signal transmission system comprising a transmission line witha plurality of repeaters in tandem, giving rise to modulation voltages,means providing that the total modulation voltage for the line at agiven frequency shall not exceed a predetermined value E1, meanscomprising a plurality of phase equalizers equally spaced and dividingthe line into a plurality of equal sections in each of which thegenerated modulation voltage is E, the phase equalizer being of suchcharacter as to introduce a phase shift between the modulation voltagegenerated in one section and the analogous modulation voltage ar-'riving from the previous section equal to or greater than that given by13. The combination of claim 12 characterized by the fact that the phaseequalizers are placed at each repeater.

14. The combination of claim 8 characterized by the fact that there is aphase correcting network at one point in the line to compensate for theplurality of phase distortions given to the desired signal by theplurality of phase distorters.

15. The combination of claim 12 characterized by the fact that there isa phase correcting network at one point in the line to compensate forthe plurality of phase distortions given to the desired signal by theplurality of phase equalizers.

1G. The combination of claim 12 combined with means at a repeaterstation to compensate for uncontrolled variations in phase frequencyrelationship of a section of the transmission line.

17. The combination of claim 12 combined with means at a repeaterstation to automatically compensate for uncontrolled variations in themodulation generated in the repeater section.

18. In a signal transmission system comprising a transmission line witha plurality of repeaters in tandem each giving rise to a modulationvoltage of a given frequency of a value Er from a plurality ofmodulation sources, the method of keeping the modulation voltage at thatfrequency for the transmission line below a predetermined value E1 whichconsists in introducing in connection with each repeater section a phasefrequency distortion 0 for that frequency of such value that JOHN G.KREER, JR.

is less than E1.

